“There has to be a vision of what comes next,” President Joe Biden said last week of the war between Israel and Hamas. “In our view, it has to be a two-state solution.” The surest path to peace, said Prime Minister Rishi Sunak of Britain, is a two-state solution, a sentiment echoed by President Emmanuel Macron of France.

At first glance, their words seemed like a sepia-tinted throwback: invoking, as a remedy for the worst eruption of bloodshed between Israelis and Palestinians in many years, the faded relic of a peace process that many on both sides viewed as dead and buried some time late in the Obama administration.

And yet, the two-state solution — Israelis and Palestinians living side-by-side in their own sovereign countries — is getting a new hearing, not just in foreign-policy circles in Washington, London and Paris but also, more quietly, among the combatants themselves. In part, it reflects the lack of any other viable alternative.

“We cannot return to a pattern where every other year, there is a violent confrontation between Israel and Hamas,” said Gilead Sher, who helped lead Israel’s negotiations with the Palestinians in the late 1990s and early 2000s, when the two sides arguably came closest to striking a two-state settlement.

“If America engages in what President Biden has stated he would commit to, there is a chance,” Sher said. “There is a chance for negotiations that could provide a step-by-step process to two distinct states.”

Such an effort would have to overcome a thicket of obstacles, not least the proliferation of Jewish settlements in the West Bank, which Palestinians say have eroded the dream of creating a viable state on that land. The rise of ultranationalists in Israel further complicates the task: They oppose Palestinian statehood, seek to annex the West Bank, and know that uprooting the settlers is political dynamite.

Sher listed a string of caveats for Israeli-Palestinian talks: The two sides would have to start modestly, with a political process focused on disengagement rather than a high-stakes negotiation over the details of two states. Both would need new leaders, he said, since the existing ones have proved to be unwilling or incapable of striking a deal. Above all, Hamas would have to be vanquished and the Gaza Strip demilitarized.

Israeli officials say they are focused on the battle against Hamas, which could last for months, and that any discussion of a peace process must wait until after the guns are silent. But in think tanks and corners of the Israeli foreign ministry, discussion of what a day-after political process would look like has already begun.

Among Palestinians, suffering Israel’s bombardment and blockade of Gaza, and rising tensions on the West Bank, the prospects for statehood appear even more far-fetched. But some Palestinians argue that the shock of the Hamas attacks on Oct. 7 has stripped Israelis of the illusion that they can manage conflict with Palestinians without confronting their deeper aspirations for nationhood.

“What happened on Oct. 7 should push us to be more creative and more innovative about the two-state solution,” said Nidal Foqaha, director general of the Palestinian Peace Coalition, a nonprofit group based in Ramallah, in the West Bank. “Without a political horizon, this is an impossible mission.”

The mechanics of such a process are far from clear. The European Union last week called for an international peace conference, an idea championed by Spain, which held a landmark Middle East peace summit in Madrid in 1991. Arab nations could also convene peace negotiations, though an early effort by Egypt last week, as the Israeli military operation in Gaza was gearing up, produced little.

By all accounts, the United States would have to take a central role in any talks between the Israelis and Palestinians. That has not happened since the Obama administration, when the secretary of state at the time, John Kerry, shuttled between the two sides in 2013 and 2014 before giving up in frustration. It was a quest that even then, some aides to President Barack Obama viewed as quixotic.

Under President Donald Trump, the United States shifted its energy from resolving the Palestinian issue to normalizing relations between Israel and its Arab neighbors. That strategy dovetailed with Prime Minister Benjamin Netanyahu, who was in a coalition with right-wing partners who openly disdained the idea of a Palestinian state. Netanyahu has swung between saying he would be willing to consider a Palestinian nation with limited security powers, and opposing it outright.

“One of the biggest issues with the phrase ‘two-state solution’ is that it fails to address the very real threats against Israel that exist now, and will likely continue to exist, within certain segments of Palestinian society and elsewhere,” said Jason D. Greenblatt, who was Trump’s special envoy to the region.

Greenblatt said the Trump administration’s approach to peacemaking emphasized Israel’s security needs. The Abraham Accords, the Trump-brokered deal under which Israel normalized relations with the United Arab Emirates and Bahrain in 2020, forestalled an Israeli plan to annex 30% of the West Bank. But it effectively set aside the goal of a Palestinian state.

Despite its fealty to the dream of two states, the Biden administration largely adopted the Trump blueprint. It had been trying to broker a deal that would normalize relations between Israel and Saudi Arabia, an even greater prize for Israel than the Gulf emirates, given Saudi Arabia’s status as the vanguard of the Arab world.

Those talks have been put on hold by the Israel-Hamas war. But if Israel were able to revive them, that could put the two-state solution back on the table. The Saudis have told Secretary of State Antony Blinken that they want steps toward a Palestinian state to be part of any normalization accord with Israel.

Arab countries are also likely to push for the Palestinian issue to be addressed as a condition of playing a role in stabilizing and rebuilding postwar Gaza. Dangling the prospect of a Palestinian state could reassure Egypt and Jordan, which are alarmed by the prospect of millions of refugees from Gaza.

“Part of this is to give them the framing, the packaging, they need to take part in a solution for Gaza,” said Ghaith Al-Omari, a senior fellow at the Washington Institute for Near East Policy, a research organization. “That’s one reason I think the president talked about it, even if it seemed irrelevant.”

The odds of progress with the current Israeli and Palestinian leaders are nonexistent, Al-Omari said. Netanyahu’s governing coalition includes ultranationalist partners who want to annex the West Bank, which Israel has occupied since 1967 and which they refer to by the biblical names of Judea and Samaria.

At a minimum, his government was committed to rapidly expanding the number of Jewish settlements in the West Bank. Since the Hamas attacks, attacks on Palestinians by settlers and Israeli troops have surged.

The president of the Palestinian Authority, Mahmoud Abbas, 87, has lost legitimacy with his public, analysts said, particularly after he canceled elections in 2021. Critics say Netanyahu contributed to the weakening of the Palestinian Authority by pursuing a divide-and-conquer strategy that bolstered Hamas.

Diplomatic historians like to point out that the leader of the Palestine Liberation Organization, Yasser Arafat, came tantalizingly close to a deal with Israel brokered by President Bill Clinton in 2000, only to walk away. And that was before hundreds of thousands of new settlers put down roots across the West Bank.

Violent clashes between Israelis and Palestinians have cut both ways in terms of influencing subsequent peace efforts. The barbaric nature of the Hamas attacks and the ferocity of the Israeli military response in Gaza, experts said, makes the coming debate in Israel particularly unpredictable.

“There will be two sides to that debate,” said Dennis B. Ross, a peace negotiator under Clinton and Obama. “What Hamas showed is that it is too dangerous to have a Palestinian state next to us because it could become dominated by groups like Hamas. The countervailing argument will be, once we defeat Hamas, we cannot freeze the situation with the Palestinians on our terms indefinitely.”

Al-Omari, who once advised Palestinian negotiators, suggested a less calculated reason for the reemergence of the two-state solution.

“This is similar to 9/11 in that everyone knows something huge has happened and there are going to be changes, but no one knows what the changes are going to be,” he said. “You default to your muscle memory; you default to your talking points. It’s a placeholder while you figure out what will happen.”